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UNCONDITIONAL ERROR ANALYSIS OF VEMS FOR A GENERALIZED NONLINEAR SCHRODINGER EQUATION

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Journal of Computational Mathematics 2024年第2期42卷 500-543页

作者： meng Li Jikun Zhao Shaochun Chen School of Mathematics and Statistics Zhengzhou UniversityZhengzhouHenan 450001China

In this work,we focus on the conforming and nonconforming leap-frog virtual element methods for the generalized nonlinear Schrodinger equation,and establish their unconditional stability and optimal error *** constructing a time-discrete system,the error between the solutions of the continuous model and the numerical scheme is separated into the temporal error and the spatial error,which makes the spatial error τ-*** inverse inequalities in the existing conforming and new constructed nonconforming virtual element spaces are utilized to derive the L^(∞)-norm uniform boundedness of numerical solutions without any restrictions on time-space step ratio,and then unconditionally optimal error estimates of the numerical schemes are obtained *** needs to be emphasized is that if we use the pre-existing nonconforming virtual elements,there is no way to derive the L^(∞)-norm uniform boundedness of the functions in the nonconforming virtual element spaces so as to be hard to get the corresponding inverse ***,several numerical examples are reported to confirm our theoretical results.

关键词： Conforming and nonconforming Virtual element methods Leap-frog scheme Generalized nonlinear Schrodinger system Unconditionally optimal error estimates

In memoriam:Shizhu Wen(1932-2023)

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Friction 2024年第7期12卷 1341-1346页

作者： Jianbin LUO Yonggang meng Yu TIAN State Key Laboratory of Tribology in Advanced Equipment Tsinghua UniversityBeijing 100084China

Professor Shizhu Wen,the winner of the 2015 Tribology Gold Medal,passed away due to illness on November 3,2023,at the age of *** was a professor of Tsinghua University,an academician of the Chinese Academy of Sciences,and the Honorary President of the Chinese Tribology Institute(CTI)from 1997 to *** Wen was born in 1932 in Jiangxi Province of China and graduated from Tsinghua University in 1955,where he was awarded the Outstanding Graduate Gold Medal and then remained as an assistant professor at the *** Wen was promoted to full professor in *** had undertaken tribology research at the Imperial College London in 1979 and *** 1985,he presided over the establishment of the State Key Laboratory of Tribology(SKLT)of Tsinghua University and served as the first director of the SKLT.

关键词： sided professor zhu

Deciphering and integrating invariants for neural operator learning with various physical mechanisms

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National Science Review 2024年第4期11卷 111-122页

作者： Rui Zhang Qi meng Zhi-Ming Ma Academy of Mathematics and Systems Science Chinese Academy of Sciences(CAS) Microsoft Research

Neural operators have been explored as surrogate models for simulating physical systems to overcome the limitations of traditional partial differential equation(PDE) solvers. However, most existing operator learning methods assume that the data originate from a single physical mechanism, limiting their applicability and performance in more realistic scenarios. To this end, we propose the physical invariant attention neural operator(PIANO) to decipher and integrate the physical invariants for operator learning from the PDE series with various physical mechanisms. PIANO employs self-supervised learning to extract physical knowledge and attention mechanisms to integrate them into dynamic convolutional *** to existing techniques, PIANO can reduce the relative error by 13.6%–82.2% on PDE forecasting tasks across varying coefficients, forces or boundary conditions. Additionally, varied downstream tasks reveal that the PI embeddings deciphered by PIANO align well with the underlying invariants in the PDE systems, verifying the physical significance of PIANO.

关键词： neural operator PDE solver contrastive learning physical invariants

Experimental Study on the Variation of Optical Imaging Characteristics with Zenith Angle due to Internal Solitary Waves in Sunglint

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Journal of Ocean University of China 2024年第4期23卷 943-952页

作者： LIU Tengfei SUN Lina CHANG Zhe ZHANG meng LIANG Keda meng Junmin WANG Jing School of Physics and Optoelectronic Engineering Ocean University of ChinaQingdao 266100China First Institute of Oceanography Ministry of Natural ResourcesQingdao 266061China Technology Innovation Center for Ocean Telemetry Ministry of Natural ResourcesQingdao 266061China

Internal solitary waves(ISWs)change the roughness of the sea surface,thus producing dark and bright bands in optical ***,reasons for changes in imaging characteristics with the solar zenith angle remain *** this paper,the optical imaging pattern of ISWs in sunglint under different zenith angles of the light source is investigated by collecting optical images of ISWs through physical *** experiment involves setting 10 zenith angles of the light source,which are divided into area a the optical images of ISWs in the three areas show dark-bright mode,single bright band,and bright-dark mode,which are consistent with those observed by optical remote *** addition,this study analyzed the percentage of the dark and bright areas of the bands and the change in the relative gray difference and found changes in both areas under different zenith angles of the light *** MODIS and ASAR images display a similar brightness-darkness distance of the same ***,the relationship between the brightness-darkness distance and the characteristic half-width of ISWs is determined in accordance with the eKdV theory and the imaging mechanism of ISWs of the SAR ***,the relationship between them in the experiment is almost consistent with the theoretical result.

关键词： internal solitary waves optical imaging characteristic laboratory simulation zenith angle sunglint

Covariate-Assisted Matrix Completion with Multiple Structural Breaks

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Journal of Systems Science & Complexity 2024年第2期37卷 692-728页

作者： meng Jing FENG Long ZOU Changliang WANG Zhaojun School of Statistics and Data Science KLMDASRLEBPSand LPMCNankai UniversityTianjin 300071China

In matrix completion,additional covariates often provide valuable information for completing the unobserved entries of a high-dimensional low-rank matrix *** this paper,the authors consider the matrix recovery problem when there are multiple structural breaks in the coefficient matrix β under the column-space-decomposition model A=Xβ+B.A cumulative sum(CUSUM)statistic is constructed based on the penalized estimation of β.Then the CUSUM is incorporated into the Wild Binary Segmentation(WBS)algorithm to consistently estimate the location of ***,a nearly-optimal recovery of A is *** findings are further corroborated via numerical experiments and a real-data application.

关键词： Additional covariates matrix completion multiple structural breaks wild Binary Segmentation

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Compound Product of Hypermatrices

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Journal of Systems Science & Complexity 2024年第1期37卷 169-183页

作者： CHENG Daizhan meng Min ZHANG Xiao JI Zhengping Key Laboratory of Systems and Control Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China Department of Control Science and Engineering School of Electronics and Information EngineeringTongji UniversityShanghai 201210China National Center for Mathematics and Interdisciplinary Sciences Chinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100149China.

The semi-tensor product(STP)of matrices is generalized to multidimensional arrays,called the compound product of *** product is first defined for three-dimensional hypermatrices with compatible orders and then extended to general *** different types of hyperdeterminants are introduced and certain properties are *** Lie groups and Lie algebras corresponding to the hypermatrix products are ***,these results are applied to dynamical systems.

关键词： Compound semi-tensor product hyperdeterminants hypereigenvalues and hypereigenvectors hypergeneral linear groups hypermatrices.

Experimental study on the variation of optical remote sensing imaging characteristics of internal solitary waves with wind speed

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Journal of Oceanology and Limnology 2024年第2期42卷 408-420页

作者： Zhe CHANG Lina SUN Tengfei LIU meng ZHANG Keda LIANG Junmin meng Jing WANG School of Physics and Optoelectronic Engineering Ocean University of ChinaQingdao 266100China First Institute of Oceanography Ministry of Natural ResourcesQingdao 266061China Technology Innovation Center for Ocean Telemetry Ministry of Natural ResourcesQingdao 266061China

Optical remote sensing has been widely used to study internal solitary waves(ISWs).Wind speed has an important effect on ISW imaging of optical remote *** light and dark bands of ISWs cannot be observed by optical remote sensing when the wind is too *** relationship between the characteristics of ISWs bands in optical remote sensing images and the wind speed is still *** influence of wind speeds on the characteristics of the ISWs bands is investigated based on the physical simulation experiments with the wind speeds of 1.6,3.1,3.5,3.8,and 3.9 m/*** experimental results show that when the wind speed is 3.9 m/s,the ISWs bands cannot be observed in optical remote sensing images with the stratification of h_(1)∶h_(2)=7∶58,ρ_(1)∶ρ_(2)=1∶*** the wind speeds are 3.1,3.5,and 3.8 m/s,which is lower than 3.9 m/s,the ISWs bands can be obtained in the simulated optical remote sensing *** location of the band’s dark and light extremum and the band’s peak-to-peak spacing are almost not affected by wind ***-significant wind speeds can cause a greater gray difference of the light-dark *** provided a scientific basis for further understanding of ISW optical remote sensing imaging.

关键词： internal solitary wave(ISW) optical remote sensing wind speed characteristics of ISWs bands

Modeling Long- and Short-Term Service Recommendations with a Deep Multi-Interest Network for Edge Computing

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Tsinghua Science and Technology 2024年第1期29卷 86-98页

作者： Rui Yuan Shunmei meng Ruihan Dou Xinna Wang Department of Computer Science and Engineering Nanjing University of Science and TechnologyNanjing 210056China Faculty of Mathematics University of WaterlooWaterloo N2L 3G1Canada

Edge computing platforms enable application developers and content providers to provide context-aware services(such as service recommendations)using real-time wireless access network *** to recommend the most suitable candidate from these numerous available services is an urgent ***-through rate(CTR)prediction is a core task of traditional service ***,many existing service recommender systems do not exploit user mobility for prediction,particularly in an edge computing *** this paper,we propose a model named long and short-term user preferences modeling with a multi-interest network based on user *** uses a logarithmic network to capture multiple interests in different fields,enriching the representations of user short-term *** terms of long-term preferences,users'comprehensive preferences are extracted in different periods and are fused using a nonlocal *** experiments on three datasets demonstrate that our model relying on user mobility can substantially improve the accuracy of service recommendation in edge computing compared with the state-of-the-art models.

关键词： recommender system logarithmic network nonlocal network

Dynamic performance and parameter optimization of a half-vehicle system coupled with an inerter-based X-structure nonlinear energy sink

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Applied Mathematics and Mechanics(English Edition) 2024年第1期45卷 85-110页

作者： Yong WANG Peili WANG Haodong meng Liqun CHEN .Automotive Engineering Research Institute Jiangsu UniversityZhenjiang 212013Jiangsu ProvinceChina Guangxi Key Laboratory of Automobile Components and Vehicle Technology Guangxi University of Science and TechnologyLiuzhou 545006Guangxi Zhuang Autonomous RegionChina School of Automotive Engineering Changzhou Institute of TechnologyChangzhou 213032Jiangsu ProvinceChina Shanghai Key Laboratory of Mechanics in Energy Engineering Shanghai Frontier Science Center of MechanoinformaticsShanghai Institute of Applied Mathematics and MechanicsSchool of Mechanics and Engineering ScienceShanghai UniversityShanghai 200444China

Inspired by the demand of improving the riding comfort and meeting the lightweight design of the vehicle, an inerter-based X-structure nonlinear energy sink(IXNES) is proposed and applied in the half-vehicle system to enhance the dynamic performance. The X-structure is used as a mechanism to realize the nonlinear stiffness characteristic of the NES, which can realize the flexibility, adjustability, high efficiency, and easy operation of nonlinear stiffness, and is convenient to apply in the vehicle suspension, and the inerter is applied to replacing the mass of the NES based on the mass amplification characteristic. The dynamic model of the half-vehicle system coupled with the IX-NES is established with the Lagrange theory, and the harmonic balance method(HBM) and the pseudo-arc-length method(PALM) are used to obtain the dynamic response under road harmonic excitation. The corresponding dynamic performance under road harmonic and random excitation is evaluated by six performance indices, and compared with that of the original half-vehicle system to show the benefits of the IX-NES. Furthermore, the structural parameters of the IX-NES are optimized with the genetic algorithm. The results show that for road harmonic and random excitation, using the IX-NES can greatly reduce the resonance peaks and root mean square(RMS) values of the front and rear suspension deflections and the front and rear dynamic tire loads, while the resonance peaks and RMS values of the vehicle body vertical and pitching accelerations are slightly *** the structural parameters of the IX-NES are optimized, the vehicle body vertical and pitching accelerations of the half-vehicle system could reduce by 2.41% and 1.16%,respectively, and the other dynamic performance indices are within the reasonable ***, the IX-NES combines the advantages of the inerter, X-structure, and NES, which improves the dynamic performance of the half-vehicle system and provides an effective option for vibrati

关键词： inerter X-structure nonlinear energy sink(NES) half-vehicle system dynamic performance